A COUPLED RESONATOR REFLEX KLYSTRON 727 



to the repeller-drift-angle, a condition which in most practical cases 

 holds over a restricted repeller voltage swing about its midmode value, 

 then the repeller voltage-frequency plot ^vill have the same shape as 

 the input phase angle-frequency curve of the passive circuit, differing 

 from the latter only by a constant multiplying factor. We therefore 

 conclude that the modulation performance of the reflex klystron, at 

 least over the central portion of the mode, may be predicted from an 

 examination of the driving point properties of the passive circuit. 



The above method of graphical analysis is quite useful in the case of 

 conventional reflex klystrons, although the same results may be ob- 

 tained analytically by making use of the equation for electronic admit- 

 tance in conjunction with that of the input admittance of a single 

 resonator. In the case of coupled resonators the expression for input 

 admittance becomes much more involved, as we shall see later, Avith 

 the result that the graphical approach outlined above was found by 

 far the quicker and more practical method of solution. 



3.0 THEORY OF COUPLED RESONATOR REFLEX KLYSTRON 



It has been shown that the performance of a reflex klystron can be 

 analyzed by considering the electronic and passive circuit admittances 

 separately and then combining the two graphically in the complex 

 admittance plane. The same procedure can be adopted in the deter- 

 mination of mode shapes resulting from the interaction of the electronic 

 admittance with any arbitrary circuit admittance which can be realized 

 across the gap. Conversely, we can determine the admittance or im- 

 pedance function required to produce a particular desired mode shape. 

 In other words: given an admittance function, we can determine the 

 resulting mode shape, and given a desired mode shape, we can predict 

 the required admittance function. As an example, consider a mode 

 having a flat top and vertical sides as shown in Fig. 5(a). This would be 

 the ideal shape for a reflex oscillator to be used as an electronically swept 

 signal source. To achieve this mode shape, we must realize an admit- 

 tance function across the bunching grids yielding a constant excess of 

 negative electronic admittance over a range of repeller voltages. Such 

 a function is shown in the complex admittance plane along with the 

 plot of Yes in Fig. 5(b) and the corresponding input impedance in 5(c). 

 It ^vill result in a frequency range of constant RF gap voltage which in 

 turn mil give rise to a range of flat power provided it is developed across 

 a constant, frequency-invariant conductance. In order to clarify this 

 rather important consideration, let us write the admittance appearing 



